Nonlinear Dynamics of Memristor Oscillators

Corinto, Fernando; Ascoli, Alon; Gilli, Marco

doi:10.1109/tcsi.2010.2097731

Cited by 309 publications

(151 citation statements)

References 20 publications

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“…Following [4] memristors are two-terminal electronic passive devices for which a nonlinear relationship links charge and flux [3]. They seem to be at the basis of future generation oscillatory associative and dynamic memories; as another important feature, nanoscale memristors have potential to reproduce the behavior of biological synapses.…”

Section: Theoremmentioning

confidence: 99%

Uniqueness and Non-uniqueness of Limit Cycles for Piecewise Linear Differential Systems with Three Zones and No Symmetry

Llibre

Ponce²,

Valls

2015

J Nonlinear Sci

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Abstract. Some techniques for proving the existence and uniqueness of limit cycles for smooth differential systems, are extended to continuous piecewiselinear differential systems. Then we obtain new results on the existence and uniqueness of limit cycles for systems with three linearity zones and without symmetry. We also reprove existing results of systems with two linearity zones giving shorter and clearer proofs.

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Section: Theoremmentioning

confidence: 99%

Uniqueness and Non-uniqueness of Limit Cycles for Piecewise Linear Differential Systems with Three Zones and No Symmetry

Llibre

Ponce²,

Valls

2015

J Nonlinear Sci

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“…Analogously, the first row of the Q-matrix leads to and this is Kirchhoff's current law for the fundamental cutset defined by R\ (cf. (19)). The running example is also useful to illustrate Lemma 1.…”

Section: Fundamental Matricesmentioning

confidence: 99%

“…System (37) has two peculiar features. First, equilibria are not isolated, defining instead an equilibrium surface given by q mc = Lp m i = 0 (lines of equilibria have been already observed in circuits with memristors [10,19,26]). Second, the dynamics is foliated by a family of invariant surfaces which is parameterized by two constants fa, fa-To see this, recast ( The two-dimensional dynamics in such invariant surfaces can be described in terms of a mc and p m i from (37a) and (37c), namely…”

Section: Dynamical Features Of a Family Of R-mc-ml Circuitsmentioning

confidence: 99%

Second order mem‐circuits

Riaza

2014

Circuit Theory & Apps

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This paper presents a comprehensive taxonomy of so-called second order memory devices, which include charge-controlled memcapacitors and flux-controlled meminductors, among other novel circuit elements. These devices, which are classified according to their differential and state orders, are necessary to get a complete extension of the family of classical nonlinear circuit elements (resistors, capacitors, inductors) for all possible controlling variables. Using a fully nonlinear formalism, we obtain nondegeneracy conditions for a broad class of second order mem-circuits. This class of circuits is expected to yield a rich dynamic behavior; in this regard we explore certain bifurcation phenomena exhibited by a family of circuits including a charge-controlled memcapacitor and a flux-controlled meminductor, providing some directions for future research.

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“…Since the successful fabrication of physical memristive device by the scientists at Hewlett-Packard Labs in 2008 (Strukov et al 2008), witch its existence was firstly predicted by Leon Chua in 1971(Chua 1971, various types of models of networks based on memristor have been designed and analyzed (Itoh and Chua 2010;Oskoee and Sahimi 2011;Corinto et al 2011;Buscarino et al 2012;Pershin and Ventra 2012;Pershin et al 2013;Yang et al 2014;Qi et al 2014). Especially, the memristor-based neural networks has been one of the most active research areas and has attracted the attention of many researchers (Itoh and Chua 2010;Pershin and Ventra 2012;Yang et al 2014;Qi et al 2014;Chandrasekar et al 2014;Wan and Cao 2015).…”

Section: Introductionmentioning

confidence: 99%

Function projective synchronization of memristor-based Cohen–Grossberg neural networks with time-varying delays

2015

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This paper deals with the problem of function projective synchronization for a class of memristor-based Cohen-Grossberg neural networks with time-varying delays. Based on the theory of differential equations with discontinuous right-hand side, some novel criteria are obtained to realize the function projective synchronization of addressed networks by combining open loop control and linear feedback control. As some special cases, several control strategies are given to ensure the realization of complete synchronization, anti-synchronization and the stabilization of the considered memristor-based CohenGrossberg neural network. Finally, a numerical example and its simulations are provided to demonstrate the effectiveness of the obtained results.

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Nonlinear Dynamics of Memristor Oscillators

Cited by 309 publications

References 20 publications

Uniqueness and Non-uniqueness of Limit Cycles for Piecewise Linear Differential Systems with Three Zones and No Symmetry

Uniqueness and Non-uniqueness of Limit Cycles for Piecewise Linear Differential Systems with Three Zones and No Symmetry

Second order mem‐circuits

Function projective synchronization of memristor-based Cohen–Grossberg neural networks with time-varying delays

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